证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α

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证明题:sin(-α)sin(丌-α)-tan(-α)cot(α-丌)-2cos^2(-α)+1=sin^2α证明题:sin(-α)sin(丌-α)-tan(-α)cot(α-丌)-2cos^2(-α

证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α
证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α

证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α
sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1
=-sin²α+1-2cos²α+1
=-sin²α+2-2cos²α
=sin²α+2sin²α
=sin²α
得证

sin(π-α)=sinα ∴sin(-α)sin(丌-α)=—sin^2(α)
tan(-α)cot(α-丌)=—1
2cos^2 (-α)=2cos^2 (α)
∴左边=—sin^2(α)+1—2cos^2 (α)+1=1—cos^2 (α)=sin^2(α) =右边